The Rosh (Hilchos sefer Torah 3) quotes Rabbeinu Baruch as holding that pigul can only be violated if it is done with dibur, meaning that one articulates the pigul, but machshava alone doesn't create pigul. The Rambam (Pesulei Hamukdashin 18:1) disagrees and holds that pigul can be violated by the mere thought of chutz l'zmano. In our gemara we are trying to find a case where something would be a violation of pigul by kodshim but not a violation of a machshava of avoda zara by chulin. The gemara says that if machshava of avoda zara wouldn't invalidate the animal by chulin, then what would be a case where one does shechita for avoda zara. Tosafos says that if pigul can b e violated through machshava (Rambam), then we have a simple case where pigul is a problem by kodshim but machshava for avoda zara wouldn't be a problem by chulin - because machshava for avoda zara without dibur wouldn't invalidate the animal, but with dibur it would. Tosafos seems to be uncertain whether pigul requires machshava or dibur.
In Baba Metzia 43b Tosafos seems to assume like the Rosh that pigul needs dibur, whereas the gemara in gittin 53a seems to hold that one does require dibur by comparing pigul to hezek sh'eino nikar, yet distinguishes between hezek sh'eino nikar and pesulim of machshava.
The Rashash on 39b writes that if we require dibur for pigul, then we should also require dibur when one shechts chulin for avoda zara, otherwise the kal v'chomer of R. Yossi doesn't make sense because there would be a pircha that pigul is only violated with dibur. The Rashash points out that the gemara seems to understand that shechita for avoda zara wouldn't require dibur because we apply the concept of הוכיח סופו על תחילתו, meaning that machshava afterward reflects on the shechita. This would only make sense if it is a p'sul of machshava but doesn't make sense if it is a p'sul of dibur. Therefore, it should follow that pigul can be violated even with machshava.
To be explain the opinion of the Rosh, it seems that the concept of dibur by pigul isn't a din of dibur similar to kriash shema and kiddush, rather it is a din to have a machshava with a gemiras da'as that is only achieved through dibur. The function of the dibur is to be me'galeh that there was a clear machshava. Therefore, even according to the Rosh that dibur is necessary, the concept of הוכיח סופו על תחילתו would still make sense since the core p'sul is a p'sul of machshava, and the dibur is only a verification of that machshava. A similar sevara can be used to explain the function of dibur in sefiras ha'omer and when making a neder.